A pseudo-elastic model for loading, partial unloading and reloading of particle-reinforced rubbe

Particle-reinforced rubbers exhibit a marked stress softening during unloading after loading in uniaxial tension tests, i.e. the stress on unloading is significantly less than that on loading at the same stretch. This hysteretic behaviour is not accounted for when the mechanical properties are represented in terms of a strain-energy function, i.e. if the material is modelled as hyperelastic. In this paper a theory of pseudo-elasticity is used to model loading, partial or complete unloading and the subsequent reloading and unloading of reinforced rubber. The basis of the model is the inclusion in the energy function of a variable that enables the energy function to be changed as the deformation path changes between loading, partial unloading, reloading and any further unloading. The dissipation of energy, i.e. the difference between the energy input during loading and the energy returned on unloading is accounted for in the model by the use of a dissipation function, the form of which changes between unloading, reloading and subsequent unloading